The validity of Beurling theorems in polydiscs

Mandrekar, V.

doi:10.1090/S0002-9939-1988-0938659-7

The validity of Beurling theorems in polydiscs
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Proc. Amer. Math. Soc. 103 (1988), 145-148 Request permission

Abstract:

This paper gives necessary and sufficient conditions for an invariant subspace $\mathcal {M}$ of ${H^2}({T^2})$ to be of the form $q{H^2}({T^2})$ ($q$ inner) in terms of double commutativity of the shifts. Recent results in [8] follow directly from our work. Relation to the work in [1] is also discussed.

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